How Should We Understand the Core Mass Function? A memo of the CMF2IMF conference at ESO Garching

The origin of the stellar initial mass function (IMF) remains one of the central questions in astronomy. Nearly three decades ago, the resemblance between the core mass function (CMF) and the IMF inspired the community to suggest that the stellar mass spectrum might be imprinted early in molecular-cloud cores and then mapped to the IMF through a simple efficiency factor. It has become gradually clear, however, that this apparent mapping involves multiple non-linear physical processes. Motivated by the spirit of the CMF2IMF conference at ESO Garching, this memo first reviews the historical quest to understand the origin of the IMF, and then sets the stage for building a shared understanding of current CMF measurements. We therefore compile several observational core catalogues at various environments and evolutionary stages into a common framework, implemented in the public Python package CMF4All. We show that the inferred high-mass CMF slope depends strongly on the adopted minimum fitting mass. A significantly steeper slope is observed in the early-stage sample, indicating a potentially evolving mass function at the highest masses. We conclude by outlining future directions to spare more efforts for both the observational, numerical simulation, and theoretical sides.